rest on/upon

phrasal verb

rested on/upon; resting on/upon; rests on/upon

1

: to depend or rely on (someone or something)

All our hopes rested on one man.

2

: to stop moving and look at (someone or something)

His eyes/gaze rested on the letter.

3

: to be based on (something)

His theory rested upon two important pieces of evidence.